Introduction

A major challenge of the times can be framed metaphorically in terms of consumption, osmosis and circulation -- as well as their subsequent consequences. These processes have the advantage of being widely comprehensible with respect to the human body, especially given that osmosis is the process whereby oxygen from the air passes through the lungs into the bloodstream (with an equivalent in plants). The question is what these processes suggest in terms of the processing of information, insight and knowledge.

As a process, osmosis is especially significant in that society faces a major difficulty at the interface between "outside" and "inside", whether with respect to outgroups and ingroups, marginal and mainstream disciplines, or insights restricted to the few which are transferable to the many only with difficulty (as may be true of the reverse). There are obviously major social issues with regard to being on the "inside" (namely "in the loop") or on the "outside" ("out of the loop"). The emerging concern with recycling suggests that there are major difficulties that could be usefully understood in terms of the system of consumption and waste disposal.

The widepread recourse to psychoactive drugs suggest that issues of "outside" and "inside" are already of deep concern, whether because of the appeal of "inside" or the consequences of alienation from "outside". Possibilities may be variously explored (World Introversion through Paracycling: global potential for living sustainably "outside-inside", 2013). Under the circumstances, the manner of current economic preoccupation with "import/export" and "input/output" suggests that these may be obscuring systemic dynamics of greater import.

Expressed otherwise, many of these matters have been extensively debated -- seemingly to questionable effect. The difficulty is partly the quantity of information and the form it takes. Have key "insights" become virtually impossible for many to injest fruitfully? Are they successfully embodied? Are they essentially indigestible? What of their ejestion when no longer appropriate?

The issue explored here is whether the challenge can be framed otherwise and more generally through patterns articulated in a different mode -- following the adage a picture is worth a thousand words. However, rather than doing this through imagery which has already been deployed to this end, the concern is whether there are patterns which have both a degree of cognitive appeal as symbols (exploiting the potential of 3D and virtual reality), as well as offering further significance from the disciplines with which they are more especially associated.

Basic to this approach is the torus and the transformations to which it lends itself -- including the unusual possibility of its eversion. Not to be forgotten is the sense in which the human body (as with many animals) can be understood as a segment of a torus -- injesting at one end, ejesting at the other, and forming part of a cyclic system in which what goes around, comes around. The concern is whether forms related to the torus and its adaptations constitute a suggestive set of complementary patterns that can be briefly indicated as a catalyst for further consideration.

One key central to this exploration is the long-valued symbol of the ouroboros -- currently used to frame the more fundmental preoccupations of cosmology. The symbol typically features a dragon-like serpent. This has the particular merit in this period of engaging popular imagination due to its extensive use in video games and fantasy movies with their improbable appropriation of a multitude of conventionally deprecated traditional symbols. What is being enabled or sought by such engagement?

The argument clarifies the poorly recognized experiential need to "proprioceive" consciously -- in contrast with a detached degree of academic interest in the topic of proprioreception as a form of cognitive appropriation. The argument highlights the potential implications of "unproprioception" arising from the ambiguity between detachment and attachment -- whether appropriate or inappropriate, as intimately related to property, its obsessive acquisition and sequestration.

Given the challenges of possession and "letting go", and the widespread preoccupation with "analysis", is this coincidentally indicative of a civilization handicapped to an unexplored degree by "anal retentiveness"?

In the light of the indications above, it would seem that clues could be sought from the following -- and more especially from the metaphors with which they are associated:

eating: whether understood simply as injesting food, masticating and swallowing -- or as in "eating up" the opposition, a new rumour (news, etc), the miles (when driving a car). The physiology of oral processing of food offers insights through labial movement, use of the teeth and tongue and peristalsis, and how these all work together to process the food prior to absorption of nutrients in the stomach. As a metaphor it may be used to frame the consumption of resources in general, and by extension to the exploitation of non-rewable resources being "eaten up". Potentially more problematic is the manner in which a group will "eat up" newcomers -- processing them from being "outsiders" to becoming "insiders" -- as with hazing rituals in educational institutions, the military and prisons. Also of relevance is the sense of "sucking meaning" out of experience, or "sucking dry" the resources of others.

breathing: whether understood in terms of respiration (inspiration, expiration) -- or as in deriving inspiration from people, media, nature, etc. The physiology offers particular insights from the operation of the lung surfaces and there are a number of available animations of that process. As a metaphor its use with respect to new information as "fresh air" is obvious, as with the effects of inhaling polluted air. There is a considerable tradition of meditation on the cognitive implications of inspiration and expiration. Whereas osmosis conventionally refers to transfer of molecules, there is some exploration of how it might be understood in terms of memes (Shane Greenup, Critical Thinking by Osmosis, Medium)

acquisition and appropriation: understood in the various senses in which possession of elements of the environment is sought and
achieved opportunistically, competitively -- "won"or "grasped" -- usefully framed through a play on words as "mining":

acquisition of property and "making a profit" -- as is typical of business and entrepreneurship

appropriation of intellectual property -- as is typical of surveillance, restrictive control of knowledge in secret, and its "classification" by security sevices and other interests

strategic acquisition and control of territory (hegemony) -- long framed in terms of military conquest and domination

sport and the achievement of eminence it offers -- notably promoted as a mark of national preeminence (as exemplified by investment in the Olympic Games)

accumulation of merit -- whether in this world or in expectaion of a life hereafter (as a primary preoccupation of Buddhism, for example)

explanation and "making sense": whether framed as the quest for knowledge by science, or as the articulation of a world view through philosopy and theology

gathering experience: whether in life skills, personal relationships, or travel to satisfy curiosity -- exemplified by tourism and the discovery it offers

education: whether understood as the acquisition of skills, self-development or as a spiritual quest

driving a vehicle: given the attentive focus to the road ahead as the driver -- or understood as driving (running) an organization, or progressing an ideological or other agenda, following a strategic pathway. These offer insights from conscious control of the driving process, speed, direction, road surface and obstacles, gradient, etc -- and engagement with them, exemplified by the phrase "let's roll". Canoeing offers a variant of the sense of driving a vehicle, notably in the light of the metaphor "pushing the river versus guiding the canoe". A contrasting variant is offered by the sense of boring a tunnel, "driving" a tunnel, and driving through it -- possibly framed in terms of expectation of the "light at the end of the tunnel".

self-promotion: to attract attention in quest of re-cognition, possibly involving "re-invention" of oneself through the image projected -- exemplified by obsession with the accumulation of "likes" on social media.

breaking wave: whether as most commonly recognized at a beach and the possibilities of surfing -- clarified by insights from fluid dynamics. In the latter case a breaking wave is one whose amplitude reaches a critical level at which some process can suddenly start to occur that causes large amounts of wave energy to be transformed into turbulent kinetic energy. At this point, simple physical models that describe wave dynamics often become invalid, particularly those that assume linear behaviour. The sense of an advancing wave or a new wave is indiciative of how encountering the future may be experienced. Used as a metaphor, it may describe the onset of some form of change -- possibily in fashion, in public opinion (as on social media), or at the onset of revolution. There is extensive use of "third wave" (as in Third-wave feminism, Third Wave Democracy, The Third Wave (1980) by Alvin Toffler).

Missing from their appreciation as distinct processes is the manner in which each may undermine qualities associated with others. This is exemplified by the sacrilegious treatment of graves by archaeologists at the service of mueseums -- totally lacking in respect for what was sought by those buried and their cultures.

Eating offers the most obvious insights into "cognitive osmosis", given the gustatory process of tasting and mouthfeel -- especially cultivated in wine tasting. The cognitive engagement in music appreciation offers another striking example. By contrast, an associated process of metaphorical significance is offered by the bidirectionality of respiration (inspiration/expiration) and eating (whether as regurgitaion or as spitting, notably a characteristic of the wine tasting process).

As seemingly disparate processes, the argument here is that these all suggest or imply the possibility of a more generic understanding, namely of how they offer complementary insights into a process which calls for cognitive appreciation. Their apparent variety invites efforts to cluster them according to drivers they variously share to different degrees, such as curiosity, possession, education. The examples may draw valuable attention to aspects of what is presumably a very complex process -- one which is non-linear and probably multidimensional in ways which call for new approaches to their visualization.

Complementary visual patterns: Ouroboros, Möbius strip, Klein bottle

The focus in the following examples is on some form of injestion dynamic. However "inappropriate", it is of course of great interest to recognize examples with respect to ejestion in a later portion of what is necessarily to be understood as a cycle. The patterns presented here are all based on the torus, derived from it, or associated with it in some way. In its more commonly recognized form as a ring or halo, its appreciation as a much-valued symbol should not be forgotten.

Whether the symbolic focus is through the sphere or the torus, of particular interest is the sense they offer of enveloping -- possibly through "graspng" and "grabbing". Related processes include:, englobing, encompassing, enwrapping, enclosing and encircircling. The latter is highlighted in the phrase "circling the wagons". Such processes variously imply a sense of embodiment -- with the possible further implication of entitlement. A particular sense of the process is offered by the processes in the game of go, whose significance with respect to the promise of artificial inelligence have been recently highlighted (AlphaGo Zero: Google DeepMind supercomputer learns 3,000 years of human knowledge in 40 days, The Telegraph, 18 October 2017).

Torus -- its inversion and eversion: Standard tori fall into four categories. namely the relatively familiar ring torus, a horn torus with the rotating circle touching the axis of rotation, or a self-intersecting spindle torus, with the sphere considered as a degenerate case. Inversions of the standard tori are known as cyclides (or Dupin cyclides), of which the ring cyclide is especially relevant to the following visualizations. Others include the horn cyclide and the spindle cyclide.

The BBC summary uses as its primary image one of a double dragon-serpent. This features with related images in an extensive account by Iona Miller (Jungian Genealogy: Jung on the Serpent). The coloured image, variously available, has been reversed and depicted in a black-white version below.

Image of double dragon-serpent Ouroboros

Reverse colour

Black-and-white

Original image from Clavis Artis, an 18th century manuscript on alchemy attributed to Zoroaster
(Biblioteca dell'Academia Nazionale dei Lincei, Rome)

The symbol continues to be widely valued in jewellry and iconography, with many imaginative variants in torcs, pendants and clasped bracelets. Of considerable significance in this respect is its appeal as a symbol by-passing a plethora of explanations and commentary. However it is the manner in which the intertwining of its elements is explored that merits recognition of an intuitive appreciation of forms of complexity understood through symmetry. Some forms recall the widely recognized symbol of infinity with which the ouroboros is closely associated. That on the right below recalls the association with the dream of August Kekulé enabling the discovery of the structure of the benzene molecule so fundamental to organic life.

Contrasting depictions of the ouroboros -- and its associations with infinity symbol

The relation between two dragons in variants of the symbol can be usefully compared with continuing popular appreciation of the dragon dance of Chinese culture. The dragon is often led by a person holding a spherical object representing a pearl. There are many depictions of intertwined dragons in pursuit of a pearl. Other cultures have engendered comparable symbols as with references to a pair of serpents. The omphalos in the temple of Apollo in Delphi is associated with the myth of the meeting point of two eagles sent by Zeus. Images of the Mayan deity Quetzalcoatl tend to be considered comparable to the ouroboros.

The coiling of two serpents around an axial rod forming the caduceus dates from the Mesoptamian deity Ningishzida and has associations with trade, eloquence, negotiation, alchemy and wisdom. [As a symbol of healthcare, it has been mistakenly appropriated as a symbol of medicine in modern times -- confused with the Rod of Asclepius of Greek mythology, the internationally recognized symbol of medicine, but having only a single serpent.]

The DNA helix gave 20th-century biology its symbol, but the more we learn, the more life circles back to an older image... The helix is too well-established an icon to be deposed any time soon. And yet, a simple loop would be a much more universal symbol of how life works at all of its scales and levels. Perhaps the Ouroboros, beloved of gnostics and alchemists, has been an ideal symbol waiting in the wings for centuries: there can surely be no more evocative symbol of feedback than a snake growing by devouring its own tail.

The Triple Helix approach has been recently extended to advocacy of Quadruple Helix and Quintuple Helix models. To the extent that such helices constitute a contemporary recognition of cognitive "serpents" between which communication has been inadequate, the ouroboros may well be understood as potentially made up of multiple strands between which osmosis of some kind is required (as further discussed below).

Rosen is especially articulate with respect to the process of proprioception in relation to phenomenology and -- following the inspiration of David Bohm -- with the implications for proproceptive dialogue (Practicing Proproceptive Dialogue, Embodying Cyberspace). Proprioception is discused further below.

Configuration and animation possibilities in 3D

The concern in what follows relates to the possibility that new forms of animation may render more comprehensible the interface between "insight" and "outside" in support of intuitive experience of that interface. The idea is that beyond conventional representations of the Klein bottle, and the subtlety of its 4D implication, there may be other forms to be explored as a stimulus to the imagination. Especially relevant to this possibility is that an animation of any symbol in virtual reality allows the user to interact with it and to shift the perspective to a variety of viewpoints, notably those within the form intimately related to any understanding of injestion or ejestion and of "cognitive osmosis". Such a feature cannot be enabled with such facility in relation to the Klein bottle or the perspectival marvels of M. C. Escher.

The sketch on the left below indicates one possibility using a toroidal ring. The two "heads" may be understood as moving in relation to that ring -- along it -- with the ring passing through the head. In digesting or ejesting the ring, each mouth/head is necessarily to be understood as itself taking the form of a ring. The join between the head and the torus can be understood as continuous with the head better understood as a wave motion moving integral to the surface of the torus -- rather than the head sliding over the torus.

The adaptation of the torus as sketched below could invite far greater speculative engagement through the following images regarding the locus of "osmosis", namely in the "mouth" of a toroidal adaptation of the ouroboros. How might the process of paradoxical reversal, from outside to inside, be variously imagined? And then from inside to outside? Again, the points from which the user can view the symbol include "through the eyes of the dragon" -- if that is the preferred design metaphor, rather than as driver of a vehicle (for example).

Provisional sketch of animation of ouroboros (highlighting some design issues and questions of directionality)

The preliminary focus in what follows is the dynamics of what happens within the "mouth". However there is the further concern as to the direction in which the heads are facing, including the possibility that those directions might alternate to hold other insights. The issue in that respect is how an injesting head/mouth might function in relation to an ejesting head/mouth -- possibly more reminiscent of an anus.

Transition curve (Euler spiral / Cornu spiral / Clothoid / Spiro): The Euler spiral is a curve whose curvature changes linearly with its curve length (the curvature of the circular curve is equal to the reciprocal of the radius). Euler spirals have applications to diffraction computations. They are also widely used as track transition curves in railroad engineering/highway engineering for connecting and transiting the geometry between a tangent and a circular curve.

Track transition curve
(reproduced from Wikipedia)

The red Euler spiral is an example of an easement curve between a blue straight line and a circular arc, shown in green.

Given the problematic consequences of "linear thinking", arguably there is urgent need for "track transition" from linear to circular, and for easement curves of a psychosocial nature.

The nonconventional orientation on the left below, and the duplication on the right, are used as a very preliminary suggestion of what might be achieved with a configuration in 3D. That on the left is suggestive of how the ouroboros might have a "transitional twist" from one "head" to another. That on the right is somewhat suggestive of how the "mouths" might function.

Archimedean spiral in 3D: The Archimedean spiral (also known as the arithmetic spiral) is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Fundamental to the design of a scroll compressor (spiral compressor, scroll pump), this uses two interleaving scrolls to pump, compress or pressurize fluids such as liquids and gases. Operated in reverse, a scroll compressor is known as a scroll expander (see Scroll Expander Animation; video) , and can be used to generate mechanical work from the expansion of a fluid, compressed air or gas.

Scroll compresssor
(reproduced from Wikipedia)

Mechanism of a scroll pump with two Archimedean spirals

How might such processes be understood with respect to psychosocial "fluids" -- namely movements of opinion.

Illustrative animations in virtual reality enabled in the above by Sergey Bederov of Cortona3D

Cross-section of "Head Out"

Cross-section of "Head In "

As cross-sections it is appropriate to repeat that the Archimedean spirals for each head are a continuous 3D "lip structure" of a mouth around the torus. These depictions, together with the scroll pump/expander animations, focus attention on the nature of the "osmosis" of concern here, namely how "outside" can be understood as transformed into "inside" -- and "inside" into "outside" -- through some analogue to a semi-permeable membrane. As noted above, the obvious example is lung operation in respiration, whereby oxygen is extracted from the atmosphere and transferred into the bloodstream, and carbon dioxide is transferred from the bloodstream into the atmosphere, in a process of gas exchange.

Horn torus and cardioid in 3D: The horn torus is one of three standard tori which is however a tangent to itself at the point (0, 0, 0). The animations below are adaptations, with permission, of an animation by Wolfgang Daeumler (Horn Torus). These offer one suggestion regarding the operation of the two mouths placed in relation to the larger torus which they ingest or ejest -- although clearly the larger torus tube would then be of minimal diameter in the animations shown (effectively of zero diameter there). If it was of larger diameter, the mouths would obviously not take the form of horn-type tori, but could have a similar dynamic.

The dynamic shown below raises the further question as to whether the ring of Archimedean spiral rings forming and framing the mouth could also usefully rotate -- functioning as a vortex -- or whether the motion of the spirals within the mouth could be limited to those of scroll compressor/expander indicated above.

Illustrative animations in virtual reality enabled in the above by Sergey Bederov of Cortona3D

*** helixtor/heart_alone.x3d

Experimental animations in 3D of the ouroboros pattern

The following animation was produced as an exercise by Sergey Bederov of Cortona3D using the virtual reality modelling language (VRML). As indicated below, it may be explored with appropriate browser facilities or viewed as a video. It is based on the preliminary indications outlined above. Notable is the interactive facility to view the inside of the ouroboros by simply clicking on it. Especially remarkable (from the detail on the right) is how the transition between "outside" and "inside" is accomplished dynamically through a motion based on the Archimedean spiral "lip" design around the "mouth" (as suggested above).

As implemented above the experiment usefully highlights both various design issues and the nature of the "story" they might carry. Should the "heads" be pointing in the same direction or in opposite directions? What kind of movement of the bodies would then be appropriate? Are there other techniques for suggesting the nature of the osmosis between inside and outide?

The following exercise is based on a more schematic approach (with notably less efficient coding and the more limited aesthetics). In this case the "heads" -- pointing in the same direction -- move around the toroidal ring in such a way as to suggest that the "body" pulled behind each is of a distinctive colour. Each "mouth" then consumes what has been "embodied" by the other. It is then the "scales" on the body (better viewed in the right hand image) which change from one colour to the other as they are injested by the "mouth" which consumes them.

In this exercise, the torus contains a second torus within it. Various experiments can be made to render transparent either the "scales" around the outer torus or that torus itself -- in order to render visibile the changing pattern of variously coloured scales around the inner torus. The question is how best to highlight the transition between "inside" and "outide" which is the intended purpose of the animation. The design can be readily adapted with respect to colour of the "skin", rate of movement and design of the "head".

In its current simple form the animation is a clear illustration of an ideal recycling process in the environment. One "head" processes products enhanced by the other, degrading and ejesting them into a condition requiring reprocessing. The design of both animations can be usefully challenged by comparison with the Klein bottle as exemplifying the paradoxical "nondual duality" required by the arguments of Steven Rosen. Do the animations adequately imply the need for the 4-dimensional insight required to comprehend the Klein bottle -- through the dynamics of the animations? How might their respective animations of cognitive osmosis be challenged and improved?

From a design perspective, no particular model should necessarily be produced, but rather the focus could be more usefully placed on the development of a software template or platform inviting multiple design variations -- a template for the imagination with possibilities such as the following:

portions of spirals, as with the Fibonacci spiral or the Harriss spiral

ring cyclides, potentially especially appropriate as inversins of the torus, with alternatives illustrated by the following

Possible ring pattern variants
inspired by the ring cyclide on the left (reproduced from Wikipedia)

The systemic and cognitive significance of the four ring patterns would of course depend on whether the upper or lower interface between the halves was associated with the the injesting or ejesting locus of the head/mouth -- with the pattern on the right as possibly a hypothetical ideal. Which way is the other head pointing?

The variants offer the possibility for exploration of contrasting systemic "stories". The patterns raise valuable issues with respect to how significance is then associated with highly controversial symbolic issues of chirality and handedness. Especially problematic from symbolic, systemic and psychosocial perspectives is the controversial function of the "head/mouth" as an overtly recognized primary attractor in contrast with the powerful covert attraction exerted by the "other end" with which reproduction is associated -- and fundamental to so much psychoanalysis.

Also to be noted is that as symbols in virtual reality, these can be reoriented in a variety of ways. Clearly an animation could permit alternation between such alternative depictions.

Reproduction of the above animations here is justified in that they suggest an adaptation of the schematic animation of the ouroboros with respect to what is "encountered" cognitively when the "head" travels around the toroidal form. This is particularly appropriate to the extent that the animations above are specifically concerned with subtle cognitive processes.

A version of the schematic animation can therefore be produced to include a succession of scenes "through which" the head passes -- suggesting a succession of such processes. Similarly such use of scenes would allow the imagery associated with the cosmological depiction of the ouroboros (mentioned above) to be presented in another adaptation, most notably to highlight that scaled argument in relation to powers of 10 -- in 12 phases from 10-25 to 1030, variously depicted otherwise (Scale of the Universe: powers of ten, 1977).

Rather than the option of increasing the diameter of the scenes around the torus (left above), a different approach is possible. The scenes can be positioned within the torus as shown in the earlier animations (above centre), namely to be traversed through movement along the torus -- but within it. Further options are to vary the diameter dynamically between being visible only within and enlarged as shown above.

Strange loops: This argument derives its inspiration from the improbable processes of sphere eversion, the eversion of the torus, and from the topological transformation between sphere and torus (as illustrated in an animation above). The challenge to the imagination and to cognitive significance can be variously envisaged (Transforming vehicles of identity between global and toroidal forms, 2016).

With respect to such strangeness, the animation possibilities discussed suggest that consideration should also be given to the symbol as a whole -- with any serpents as being indicative of strange loops. One clue is offered by the pursuit of a pearl in the Chinese dragon dance. As a pearl of wisdom, this accords with the integrity implied by the ouroboros. However this can also be seen as implied by the hole which it frames and around which one or more serpents are entwined.

Holes: Such a symbolic hole merits the attention recently accorded to the mysterious nature of holes as explored by Roberto Casati and Achille C. Varzi (Holes and Other Superficialities, 1994) -- with respect to the borderlines of metaphysics, everyday geometry, and the theory of perception (reviewed by Steven A. Gross, What's in a Hole?The Harvard Review of Philosophy, 1994). Their unexpected implications are indicated in an extensive entry on holes in the Stanford Encyclopedia of Philosophy.

Such implications may be explored otherwise, as argued by Terrence Deacon as a cognitive anthropologist with respect to the role of what is missing (What's Missing from Theories of Information? 2010; Incomplete Nature: how mind emerged from matter, 2011; The importance of what is missing, New Scientist, 26 November 2011). He explores the paradoxical incompleteness of semiotic and teleological phenomena in terms of information to demonstrate how specific absences (or constraints) play the critical causal role in the organization of physical processes that generates these properties. For Deacon:

Basically, it means that our best science -- that collection of theories that presumably comes closest to explaining everything -- does not include this one most defining characteristic of being you and me. In effect, our current "Theory of Everything" implies that we don't exist, except as collections of atoms. So what's missing? Ironically and enigmatically, something missing is missing. (p. 1, emphasis added)

Directionality and wholeness: There is a curious but relatively obvious sense in which the serpents or dragons imply directionality and a quest. It is the manner in which their dynamic defines a (torioidal) ring which is intriguing -- given the relationship between torus and sphere, to the extent that the sphere is held to be more symbolic of wholeness. In conventional terms however, a sphere is essentially static rather than dynamic. What might be assumed to be the dynamics of sustainable globalization? Arguably the imagery of sphere eversion topology should inform reflection on the nature of such globalization (John M. Sullivan, Topological Stages in the Eversion; video of The Optiverse, 1998).

In their strange pursuit of wisdom, it is the serpents which embody that dynamic to a degree. Hence the potential significance of the helical, serpent-like nature of a triple, quadruple or quintuple models -- inspired by that of DNA, as noted above. As separately argued, these can be understood as engendering the symbolic stars which are so fundamental to representation of national identiy on flags and otherwise (Symbolic stars vs Strategic pillars; Polyhedra vs Helices; Logic vs Comprehension?, 2017).

Such an argument would seem to suggest a strange relationship between symbolic use of serpents, helices, stars and pillars. Are strategic stars and pillars to be usefully recognized as "frozen categories" -- "petrified" serpents, namely an "entombed" dynamic to which strategic helices are now conceived as providing a degree of remedy?

Especially intriguing in symbolic terms is the manner in which the dragon-serpents are intuitively understood to both intertwine and plunge into the hole which they thereby frame. This is strangely reminiscent of the process of intercourse and the fundamental significance attributed to it -- with a hole being the primordial attractor. It is therefore curious that the role of the double helix with respect to reproduction should now be "extended" to what is envisaged in relation to the triple, quadruple and quintuple helices -- if not more. Ironically this would seeem to anticipate the speculations of science fiction with regard to alien biologies requiring multiple sexual partners for viable fertilization. A quintuple helix model must indeed envisage 5-way cognitive osmosis. Globalization may indeed be more complex than conveniently assumed (Engendering Invagination and Gastrulation of Globalization: reconstructive insights from the sciences and the humanities, 2010).

For cosmology, it is then understandable that a theory of everything would be associated with compactification into a singular serpent -- hence the ouoboros. However, should a triple helix model be understood as a "3-serpent model" -- or a quintuple helix model as a "5-dragon model", as Chinese culture might well find appropriate in the light of Wu Xing dynamics?

The image on the right from Wikipedia, which originally appeared on the cover of Scientific American, Nov. 2007). Such manifolds are higher-dimensional analogues of K3 surfaces of significance in superstring theory. The extra dimensions of spacetime are sometimes conjectured to take the form of a 6-dimensional Calabi-Yau manifold.

The animation of the original image made use of selected aesthetic possibilities of Photoshop -- of which many others might be employed to improve the suggestive quality of the animation.

Interlocking tori: There is however also the possibility of inviting imaginative reflection on the toroidal ouroboros as a whole rather than solely on the zone of osmosis. The following animation suggests how a single head/mouth/anus might be depicted in a rendering of the more common symbol of a single serpent-dragon biting its tail. Whether the serpent is one torus or the other, the mouth/anus orifice is interlocked with it and of the same dimension -- the interlocked tori rotating with respect to one another. Such an animation offers usefully provocative and controversial connotations.

Especially intriguing is how such imagery enables anyone to identify with the "dragon" -- riding around the torus with a view from the dragon's head, as the "questing beast". How is the consumption and injestion of "otherness" ("outsideness") to be imagined -- as well as its embodiment, following transformation, into "insideness"?

Transformation? Arguments enabled by animation are no guarantee of the integrative transformation purportedly implied by the ouroboros -- Jung's Mysterium Coniunctionis (1970). The distinction may be made in the light of the imagery of the pearl of wisdom pursued in the Chinese dragon dance, assuming the dragons in the ouroboros are engaged in a dance. The pearl is then mysteriously associated with the space they surround -- the hole in the centre.

To proprioceive or not to proprioceive -- is that the question?

Whilst the noun proprioception is itself not commonly used, the verbal form (proprioceive, to propriocept?) is even more rarely used. The brain is indeed understood to dynamically integrate information from proprioceptive process and from the vestibular system into its overall sense of body position, movement, and acceleration. The word kinesthesia or kinaesthesia (kinesthetic sense) strictly means movement sense, but has been used inconsistently to refer either to proprioception alone or to the brain's integration of proprioceptive and vestibular inputs. Proprioception is often synonymous with balance. When thrown "off balance", the brain is especially challenged to propriocept.

Understandably, academics -- as academics -- have no need "to proprioceive", irrespective of the extent to which they may explain the nature of proprioception. Indicative search results at the time of writing offer: proprioception, 2,280,000; proprioceive, 1,380; to proprioceive, 349; propriocept, 39,000; to propriocept, 3,500. This is strikingly indicative of the conventional attitude to such a process, most notably in the explanatory descriptions offered by natural science and some schools of philosophy. As argued on one website: Don't Neglect to Propriocept! (Ego Performance Training, 5 March 2012).

Provocatively, a contrast may be made between widespread enthusuasm for explanation and the nature of the explaining process -- which curiously results in explanation. The latter implies a successful cognitive dissociation from the plane of reality in topological terms -- whether or not this is a complex plane. It reinforces dubious assumptions regarding global plans emerging from any planning process, speculative explored separately (Is the World View of a Holy Father Necessarily Full of Holes? 2014). Explaining could be understood as a successful cognitive disssociation from the "plain" -- as the latter is promoted in arguments for simple living.

Proprioception has the meaning to make "one's own", to take or grasp, in the sense of recognizing the relative position of one's own parts of the body and strength of effort being employed in movement. It bears an intresting relation to property, its acquisition and its possession. It is distinguished from exteroception, by the outside world is perceived, and interoception, by which pain, hunger, etc., and the movement of internal organs are perceived.

In humans, a distinction is made between conscious proprioception and non-conscious proprioception:

The intent of this thesis is to provide an account of the phenomenology of movement that collapses the distinction between mental and physical without the elimination of the mental. There are two main ways in which mental and physical converge in this account. First of all, the type of knowledge involved in learning movement skills is a type of nonpropositional knowledge that is literally embodied in the neuromuscular system of the body. Thus the mental phenomena of knowing-how and thinking how to do movement skills are body-wide phenomena. Furthermore, this type of knowledge is genuinely self-referential, since the knower and known are identical. Second, the phenomenology of self-actuated movement reveals that the self is experienced as a psychophysical unity through the experience of the coherence of action and the proprioception of that action. This is due to the sense of effort provided by sensorimotor integration of the peripheral nervous system. This sense of effort is the direct awareness of physical properties of muscle lengths, tensions, and speeds of contraction, and is thus a genuine psychophysical phenomenon. It is also argued that we enjoy a high degree of epistemic security regarding experiences of this type.

Sometimes referred to as the "sixth sense," proprioception includes the sense of position and movement of our limbs, the senses of muscle force and effort, and the sense of balance (Uwe Proske and Simon Gandevia, Proprioception: the sense within, The Scientist, September 2016). For Elise Walker:

Proprioception is a sense that we often overlook because it is only subtly distinguished from movement. And, unlike sight or hearing or taste, we rarely experience the absence of proprioception (dead arm being a rare exception). Yet, a total loss of proprioception might be even more devastating than going blind or deaf. Without sensory information coming in from our muscles, we would be unable to monitor and correct our paths of motion. Imagine trying to walk, gesture, or eat if you had no sense of where your limbs were without looking at them. Few people can understand the burden of proprioceptive loss better than an amputee. When a limb is lost, the ability to move and sense are both gone. (Proprioception: Your Sixth Sense: why movement and sensation are inextricably linked, Helix, 27 October 2014):

Informing his concern with cognitive topology, as noted above, Steven Rosen has argued extensively for a more appropriate understanding of conscious proprioception in contrast with the better known symbolic operations of perception and conception prevalent in conventional science:

Etymologically, to perceive is to "take hold of" or "take through" (from the Latin, per, through, and capere, to take), and to conceive is to "gather or take in." These activities are carried out in the "forward gear,"... The term proprioceive is from the Latin, proprius, meaning "one's own." Literally, then, proprioception means "taking one's own," which can be read as a taking of self or "selftaking." It is true that the term's conventional meaning derives from physiology, where it signifies an organism's sensitivity to activity in its own muscles, joints, and tendons. But [David Bohm (Thought as a System, 1994)] spoke of the need for "proprioceptive thought" (p. 229), which he viewed as a meditative act wherein "consciousness ... [becomes] aware of its own implicate activity, in which its content originates" (p. 232). Years earlier, the social psychiatrist Trigant Burrow spoke similarly of the need for human beings to gain a proprioceptive awareness of the organismic basis of their divisive symbolic activity (see Galt 1995). What I propose here is that a proprioceptive move is required if the dimensional organism is to gain the awareness of itself that is necessary for entering the climactic stage of its Individuation. Whereas the forward orientation of stage two maintains the trichotomy of object, space, and subject, the proprioceptive unearthing of the lifeworld carried out in stage three would disclose through its "backward" action the intimate transpermeation of these three terms. (The Self-evolving Cosmos:: a phenomenological approach to nature's unity-in-diversity, 2008) pp. 126-127) [emphasis added]

Rosen continues (pp. 245-246):

It is a commonplace of neuroscience that cognitive activity is linked to the cortical region of the brain. In Topologies of the Flesh, I drew on the work of psychiatrist Trigant Burrow to demonstrate that it is possible to proprioceive the workings of the brain. Supplementing his laboratory research with systematic self-observation, Burrow kinesthetically detected a unique pattern of tensions around the eyes and forehead that he found to be correlated with the symbolic operations of the cerebral cortex. In this experiential self-probing of the brain's "symbolic segment" (Science and Man's Behavior: the contribution of phylobiology, 1953, p. 316), the area that constitutes the site of thinking and language, Burrow was exploring the seat of his own identity as an individual governed by the thinking function.

Or, in Merleau-Ponty's terms, Burrow was investigating the "l think that must be able to accompany all our experiences" (Merleau-Ponty, 1968/1970, p. 145). Burrow himself came to refer to this cortical center of identity as the "I"-persona. This thinking subject that presides over every facet of human experience and behavior should not be confused with the ego of the allegedly isolated individual.... Therefore, when Burrow became attentive to the "I"-persona rather than continuing to be unwittingly governed by it, he experienced this palpable pattern of tension around the eyes and forehead against the "tensional pattern of the organism as a whole" (Galt 1995, p. 31). He was thus presumably able to apprehend in an immediate way what he called the "phyloorganism" (p. 445), i.e., the organism of humanity at large. Burrow coined the term "cotention" (1932) for his practice of proprioceiving the generic organism. He described the procedure as one of setting aside daily experimental periods in which he "adhered consistently to relaxing the eyes and to getting the kinesthetic 'feel' of the tensions in and about the eyes and in the cephalic area generally" (1953, p. 95). [emphasis added]

Such arguments call for greater recognition of the contrasting perspectives of proprioception, exteroception, and interoception (namely any sense that is normally stimulated from within the body). In their absence it can be readily argued that there are cognitive implications to the current environmental consequences of concreting the environment, canalizing river banks and lining tunnels.

Unproprioception: demining, mine-sweeping and waste management

As might be expected, unproprioception is not recognized as a cognitive process -- or as a valid term. Would deproprioception be a more appropriate given the increasing significance of desensitization and psychic numbing? Arguably however, with proprioception understood as a cognitive process of making externalities "one's own", the common effort to "grasp" through possessive attachment calls for recognition of the complementary process of detachment and "letting go" as may be speculatively argued (Beyond Harassment of Reality and Grasping Future Possibilities, 1996).

The process of appropriation is clearly usefully associated with proprioception -- if only etymologically through their associaion with property. Curiously that process is widely understood as "appropriate" -- despite the ambiguity from a sociopolitical perspective (Comprehension of Appropriatness, 1986).

The issue is how to recognize (appropriately) the nature of unproprioception. If proprioception can be fruitfully associated with injestion, then unproprioception should be intimately related to understandings of ejestion. As the final process in digestion, it is through defecation that organisms eliminate solid, semi-solid, or liquid waste material from the digestive tract via the anus. Again, as might be expected, both the process of infecation and that term are seldom mentioned -- despite their potential significance as metaphors for social experience, and many anecdotal comparisons of their equivalence in that respect (through questionable jargon).

Curiously again, mention of any such processes in conventional discourse tend to be framed as inappropriate -- despite being a daily feature of human biology, and however the process is then consciously experienced. Understood more generally, the process of disappropriation (as with dispossession) is readily applied to taking something away from another, but not from oneself. Whereas the verb to appropriate is widely used, no use is made of to inappropriate. The associated cognitive challenge of detachment is recognized otherwise through expressions such as "letting go" and arguments of intentional communities for simple living and voluntary poverty (as in monastic vows).

Any animation of the ouroboros therefore offers an integrative cognitive approach to the system dynamics of the alternation between attachment and detachment. Conscious engagement with this process is cultivated through schools of meditation making use of breathing exercises focusing on the cycle of inspiration and expiration. How are these insights applied to collectives?

Given the obvious relation of proprioception to the acquistion and possession of property -- with all the psychosocial controversies with which this is associated -- unproprioception as a cognitive process merits exploration in relation to "letting go", whether with respect to possessions, relationships, patterns of consumption, ideological positions, or cognitive biases (Antonio de Nicolas, Habits of Mind: an introduction to clinical philosophy, 2000; George Monbiot, Everything Must Go, The Guardian, 22 November 2017).

As noted above, this challenging cognitive process can be usefully explored through a form of word play, using "mine" as a metaphor -- given its intimate association with possession. Used as a metaphor, "mining" could then be understood as a synonym for proprioception. The complementary process could then be explored through:

mines sought possessively as a source of resources for which claims can be legally registered, often overriding other property rights. Obsession with acquisition of intellectual property could be then be understood in such terms

demining as the extremely challenging process of removing landmines from territory which has been acquired from another.

mine-sweeping as the maritime variant of demining. How indeed is the sense of "mine" to be "swept" from consciousness -- as favoured by some schools of thought?

As a process consequent on injestion, unproprioception brings into focus what is to be done with whatever is claimed as "mine". It can indeed be stored for future use -- as with the proverbial storage of nuts by a squirrel. However there is also a sense in which it involves a form of incarceration, with its particular associations to the embodiment resulting from injestion. The extent to which intellectual property is stored behind firewalls and paywalls can be usefully described as knowledge incarceration in relatively inaccessible locations. Much is made of the eventual release of classified materials.

Paradoxically, and ironically, most of the knowledge of relevance to remedial response to global lchallenges is subject, actually or potentially, to intellectual property constraints -- including research cited in this document. ***

However, further consideration of "cognitive waste management" merits exploration in the light of the major challenge of waste management on a planet of limited disposal capacity. This is exemplifed by the issues of radioactiver waste disposal and the accumulation of marine debris, most obviously in the Great Pacific Garbage Patch -- and equally symbolically through the accumulation of space debris orbiting the globe. Arguably the current global civilization, like it or not, faces a major environmental problem of "managing its shit".

Paradoxically it could be argued that global civilization has a heavy investment in the inappropriateness of having failed to "get its shit together" -- again using the common jargon phrase for emphasis. Far less evident is the management of "cognitive waste" ("cognitive shit"?) -- so evidently undermining any possibility of fruitful global governance. An animation of the ouroboros serves in some measure to highlight an appropriate degree of cognitive integration.

References

Thomas F. Banchoff and Davide P. Cervone. An Interactive Gallery on the Internet: "Surfaces beyond the third dimension". International Journal of Shape Modeling, 0, 1998 [text]